Geometry of manifold of special holonomy and gauge theory/gravity correspondence

特殊完整流形几何与规范论/引力对应

• 批准号: 14540073
• 负责人: KANNO Hiroaki
• 金额: $ 2.05万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540073/
• 关键词: exceptional holonomy; gauge theory; gravity correspondence; instanton; topological string; Seiberg-Witten theory; D-brane; 重力対応; 超対称ゲージ理論; D-ブレイン; 行列模型; Gromov-Witten不変量; 例外的ホロノミー群; M理論; ALC計量

D-branes in superstring theory provide a new method of investigating the mathematical structure of gauge theory. For example, D-branes in manifolds of exceptional holonomy group G_2,Spin(7) describe non-perturbative dynamics of supersymmetric gauge theory. In collaboration with Y.Yasui, we constructed explicit metrics of Spin(7) holonomy, that are of cohomogeneity one with SU(3)/U(1) principal orbit. In particular we found a new type of metrics that has asymptotically a circle S^1 of finite radius. This is a higher dimensional analog of four dimensional gravitational instantons ; Taub-NUT metic and Atiyah-Hitchin metic. We expect these metrics have some applications to M theory compactification.One of aims of string theory is a unification of gauge theory and gravity and gauge theory/gravity correspondence has been attracted much attention recently. When we consider topological gauge/string theory, the correspondence can be formulated mathematically more rigorous way. One of recent important achievements is instanton counting in four dimensional gauge theory by Nekrasov. In collaboration with T.Eguchi, we show that Nekrasov's partition function of instanton counting can be reproduced as a partition function of topological string theory. The partition function for SU(N) Seiberg-Witten theory is obtained by considering topological string whose target space is the ALE fibration of type A_{N-1} over P^1. Matter field can be incorporated by making a blow up on the target space. The methods used in this computation have close relations to various branches in mathematics, such as representation theory, combinatorics, knot theory and integrable systems.

超弦理论中的D-膜提供了研究规范理论数学结构的新方法。例如，例外完整群G_2，Spin（7）流形中的D-膜描述了超对称规范理论的非微扰动力学。与Y.Yasui合作，我们构造了与SU（3）/U（1）主轨道具有协齐性的Spin（7）完整性的显式度规。特别地，我们发现了一类新的度量，它渐近地具有一个有限半径的圆S^1。这是四维引力瞬子的高维类比;陶布-努特方法和阿蒂亚-希钦方法。弦理论的目标之一是统一规范理论与引力，规范理论与引力的对应是近年来引起人们广泛关注的问题。当我们考虑拓扑规范/弦理论时，对应可以用数学上更严格的方式来表达。Nekrasov的四维规范理论中的瞬子计数是最近的重要成就之一。在与T.江口的合作中，我们证明了Nekrasov的瞬子计数的配分函数可以作为拓扑弦理论的配分函数来再现。本文考虑拓扑弦，其目标空间为P^1上的A_{N-1}型ALE纤维化，得到了SU（N）Seiberg-Witten理论的配分函数。物质场可以通过对目标空间进行爆破来合并。这种计算方法与数学的各个分支有着密切的联系，如表示论、组合学、纽结理论和可积系统。

项目成果

On Spin(7) Holonomy Metric Based on SU(3)/U(1)

基于SU(3)/U(1)的Spin(7)完整度量

• 发表时间: 2002
• 期刊: Journal of Geometry and Physics 43
• 作者: H.Kanno;Y.Yasui
• 通讯作者: Y.Yasui

Properties of Some Five Dimensional Einstein Metric

某些五维爱因斯坦度量的属性

• 发表时间: 2004
• 期刊: Classical and Quantum Gravity 21
• 作者: G.W.Gibbons;S.A.Hartnoll;Y.Yasui
• 通讯作者: Y.Yasui

Whitham Prepotential and Superpotential

惠瑟姆预电势和超电势

• 发表时间: 2004
• 期刊: Nucl. Phys. B686
• 作者: Chong-Sun Chu;T.Inami;D.Y.Soa et al.;T.Inami et al.;T.Eguchi et al.;H.Itoyama et al.
• 通讯作者: H.Itoyama et al.

Symplectic fillings of the link of simple elliptic singularities

简单椭圆奇点连接的辛填充

• 发表时间: 2003
• 期刊: J. Reine Angew. Math 565
• 作者: Ohta;Hiroshi;K.Ono
• 通讯作者: K.Ono

Properties of some five dimensional Eiinstein matrics

一些五维爱因斯坦矩阵的性质

• 发表时间: 2004
• 期刊: Class.Quant.Grav. 21
• 作者: G.W.Gibbons;S.A.Hartnoll;Y.Yasui
• 通讯作者: Y.Yasui